Question

A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h = –5t2+ 92t + 16. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary. A. Reaches a maximum height of 16.00 meters in 18.4 seconds. B. Reaches a maximum height of 18.57 meters in 9.2 seconds. C. Reaches a maximum height of 37.14 meters in 18.4 seconds. D. Reaches a maximum height of 439.20 meters in 9.2 seconds.

Answer 1

D. Reaches a maximum height of 439.20 meters in 9.2 seconds.

Step-by-step explanation:

Given

h = –5t²+ 92t + 16

then

h' = 0 when the boulder reaches its maximum height

(–5t²+ 92t + 16)' = - 10t + 92 = 0

⇒ t = 92/10

⇒ t = 9.2 s

the maximum height will be

h = –5(9.2)²+ 92(9.2) + 16

h = 439.20 m